Non-Abelian Gauge Symmetry and the Higgs Mechanism in F-theory

TL;DR

The paper tackles the inadequacy of singular fiber resolution to describe spontaneous gauge symmetry breaking in F‑theory and advocates complex‑structure deformation as the correct moduli‑space branch, shared with the defining M‑theory on $X_M$. By treating gauge states as string junctions on deformed geometries, the authors develop a systematic Deformation framework for Weierstrass models, including $f$-, $g$-, and $fg$‑deformations and $\,\Delta_r$/$\Delta_i$ variants, to extract Lie algebra data from codimension one to two structures. They demonstrate new non‑perturbative realizations of $\mathfrak{su}(3)$ and $\mathfrak{su}(2)$ on stacks of four and three seven‑branes (Type IV and III fibers), while Type II fibers carry no gauge algebra; these results are tied to explicit root and representation data derived from string junctions. The approach unifies F‑theory and M‑theory perspectives, offers insights into non‑Higgsable clusters, and provides computational tools to explore the gauge content of global F‑theory compactifications, with potential phenomenological implications.

Abstract

Singular fiber resolution does not describe the spontaneous breaking of gauge symmetry in F-theory, as the corresponding branch of the moduli space does not exist in the theory. Accordingly, even non-abelian gauge theories have not been fully understood in global F-theory compactifications. We present a systematic discussion of using singularity deformation, which does describe the spontaneous breaking of gauge symmetry in F-theory, to study non-abelian gauge symmetry. Since this branch of the moduli space also exists in the defining M-theory compactification, it provides the only known description of gauge theory states which exists in both pictures; they are string junctions in F-theory. We discuss how global deformations give rise to local deformations, and also give examples where local deformation can be utilized even in models where a global deformation does not exist. Utilizing deformations, we study a number of new examples, including non-perturbative descriptions of $SU(3)$ and $SU(2)$ gauge theories on seven-branes which do not admit a weakly coupled type IIb description. It may be of phenomenological interest that these non-perturbative descriptions do not exist for higher rank $SU(N)$ theories.